Input trajectory shaping based on a B-spline model for the scanning control of a piezoelectric actuator in external-cavity diode laser

External-cavity diode lasers can continuously change the output optical frequency by scanning its optical resonant cavity (ORC), which is a piezoelectric actuated mechanical system. However, due to the hysteresis inherent in the piezoelectric actuator, the displacement response of the ORC exhibits nonlinear behaviour. In addition, the harmonics in input signal near the resonance frequencies of mechanical system will excite the vibration of the ORC. To improve the scanning characteristics of the ORC, a B-spline model is utilised to shape the input trajectory into two parts. Firstly, the nonlinearity error in the displacement response of the ORC is approximated by a B-spline model to generate a compensation voltage for the piezoelectric actuator. Secondly, the inflection-point region of the input trajectory is shaped by optimising the B-spline control points based on a frequency domain objective function to significantly reduce the energy of the resonance frequencies in input signal. The experimental results show that the B-spline shaped input trajectory significantly reduces the nonlinearity and suppresses the vibration of the displacement response of the ORC.